Automorphisms and strongly invariant relations

素模型的自同构群与不变测度

Automorphism groups of prime models, and invariant measures

本研究将饱和模型下自同构群的可定义子集概念适配到原子强齐次模型的相对自同构群，探讨其可定义子集布尔代数上不变测度的存在唯一性（稳定理论下成立），并验证该可定义性与可定义伽罗瓦上同调、微分伽罗瓦理论的相容性。

A tractable case of the Turing automorphism problem: bi-uniformly $E_0$-invariant Cantor homeomorphisms

A function $F:2^ω\to 2^ω$ is an $E_0$-isomorphism if for all $x,y\in 2^ω$, we have $xE_0y\iff f(x)E_0 f(y)$, where $xE_0y\iff(\exists a)(\forall n\ge b) x(n)=y(n)$. If such witnesses $a$ for $xE_0 y$ and for $f(x)E_0 f(y)$ depend on each other but not on $x$, $y$, then $F$ is called bi-uniform. It is shown that a homeomorphism of Cantor space which is a bi-uniform $E_0$-isomorphism can induce only the trivial automorphism of the Turing degrees.

$λ$不可达时$P(λ)/[λ]^{<λ}$的无处平凡自同构

Nowhere trivial automorphisms of $P(λ)/[λ]^{<λ}$, for $λ$ inaccessible

本文证明了当$λ$为（强）不可达基数且$2^λ= λ^+$时，布尔代数$\mathcal P(λ)/[λ]^{<λ}$存在无处平凡的自同构。

带算子的域的自同构群的单纯性

Simplicity of the automorphism group of fields with operators

本文改编 Lascar 的证明，证明了涵盖强极小理论和带算子域理论的一类不可数模型中，固定所有非泛型元素的自同构群具有单纯性。